In the study it is believed that there is a negative linear relationship between bill lengths and bill depths for the penguins. Define as the population correlation coefficient between bill length and bill depth. The appropriate null and alternative hypotheses to test are

H0:=0vsH1:0

H0:=0vsH1:<0

H0:>0vsH1:<0

H0:=0vsH1:>0

Question 2

Measurements are taken from a random selection of 12 males (4 from each species) and 12 females (4 from each species). Based on the data, the test statistic for the hypothesis test in Question 1 is -1.109. The degrees of freedom of the t distribution to be used to find the p-value is

20

22

23

24

Question 3

This study concludes that there is

weak evidence to suggest that there is a negative linear relationship between bill lengths and depths in penguins (p = 0.076)

no evidence to suggest that there is a negative linear relationship between bill lengths and depths in penguins (p = 0.140)

no evidence to suggest that there is a negative linear relationship between bill lengths and depths in penguins (p = 0.279)

no evidence to suggest that there is a negative linear relationship between bill lengths and depths in penguins (p = 0.860)

Question 4

The lower limit and the upper limit of a 95% confidence interval for population mean bill length of penguins are 43.54 mm and 47.46 mm. The margin of error is

1.34 mm

1.96 mm

2.40 mm

3.92 mm

Question 5

Now suppose that you are calculating a 90% confidence interval for population mean bill length of penguins using the same sample data as in Question 4. The 90% confidence interval will be

either narrower or wider than the 95% confidence interval

the same as the 95% confidence interval

narrower than the 95% confidence interval

wider than the 95% confidence interval

Question 6

The researchers further believe that the mean bill lengths for the 3 species are different. Define 1, 2 and 3 as the population mean bill lengths of the species Adelie, Gentoo and Chinstrap, respectively. The appropriate null and alternative hypotheses for the one-way ANOVA to test this belief are

H0:123vsH1:1=2=3

H0:1=2=3vsH1:123

H0:1=2=3vsH1:Not all population means are equal

H0:1=2=3vsH1:1>23

Question 7

The incompleteANOVA table below is for the hypothesis test in Question 6:

Source		DF	Sum Sq	Mean Sq	F value	Pr(>F)
Species			358.9
Residuals			136.9

The degrees of freedom for Species and Residuals respectively are

1,23

2,21

2,23

3,24

Based on the ANOVA table in Question 7, penguin species explains

27.6% of variability in bill lengths

32.4% of variability in bill lengths

53.0% of variability in bill lengths

72.4% of variability in bill lengths

Question 9

Using the ANOVA table in Question 7, the F statistic to test the hypotheses in Question 6 is

2.62

21.17

27.53

39.52

Question 10

Using the ANOVA table in Question 7 to test the hypothesis in Question 6, there is

no evidence to suggest that the population mean bill lengths are different among species (p > 0.1)

weak evidence to suggest that the population mean bill lengths are different among species (p < 0.1)

moderate evidence to suggest that the population mean bill lengths are different among species (p < 0.05)

strong evidence to suggest that the population mean bill lengths are different among species (p < 0.01)

Question 11

Which one of the following is NOT an assumption of the hypothesis test in Question 6?

Penguin bill lengths in each species are drawn from normally distributed populations.

Bill lengths and depths should have a linear relationship.

Population variances of bill lengths in each species are equal.

Penguin samples are random and independent.

Question 12

The researcher performs an additional analysis to examine the interaction effect of the species and the sex of penguins on their mean bill lengths. The appropriate statistical procedure is

Two-sample t-test

Wilcoxon Rank Sum test

Two-way ANOVA

Tukey's Honestly Significant Difference